Visualization of root water uptake: quantification of deuterated water transport in roots using neutron radiography and numerical modeling.

Plant Physiology Preview. Published on September 2, 2014, as DOI:10.1104/pp.114.243212

1 2

Running title: Quantification of deuterated water transport in roots

3 4

Corresponding author:

5

Mohsen Zarebanadkouki, Georg August university of Goettingen, Division of Soil

6

Hydrology, Buesgenweg 2, 37077 Goettingen, Germany, Tel: +49 (0) 551 3913517, Fax:

7

+49 (0) 551 393310, Email: [email protected]

8 9 10 11

Research area of article: Breakthrough Technologies

12 13

1 Downloaded from www.plantphysiol.org on September 7, 2014 - Published by www.plant.org Copyright © 2014 American Society of Plant Biologists. All rights reserved.

Copyright 2014 by the American Society of Plant Biologists

14

Title:

15

Visualization of root water uptake:

16

Quantification of deuterated water transport in roots using neutron radiography and

17

numerical modeling

18 19

Mohsen Zarebanadkouki (i*), Eva Kroener (i), Anders Kaestner (ii), Andrea Carminati (i)

20

(i)-Georg August university of Goettingen, Division of Soil Hydrology, Buesgenweg 2,

21

37077 Goettingen, Germany.

22

(ii)-Paul Scherrer Institute, Villigen, Switzerland

23

*Corresponding Author: [email protected]

24 25 26

Where do roots take up water from soils and how to measure it? We used neutron radiography

27

to trace the transport of deuterated water in soil and roots. By means of a numerical model,

28

we reconstructed the water flow across the root tissue and along the xylem.

29


30

Abstract

31

Our understanding of soil and plant water relations is limited by the lack of experimental

32

methods to measure water fluxes in soil and plants. Here we describe a new method to non-

33

invasively quantify water fluxes in roots. To this end, neutron radiography was used to trace

34

the transport of deuterated water (D2O) into roots. The results showed that: 1) the radial

35

transport of D2O from soil to the roots depended similarly on diffusive and convective

36

transport; 2) the axial transport of D2O along the root xylem was largely dominated by

37

convection. To quantify the convective fluxes from the radiographs, we introduced a

38

convection–diffusion model to simulate the D2O transport in roots. The model takes into

39

account different pathways of water across the root tissue, the endodermis as a layer with

40

distinct transport properties, and the axial transport of D2O in the xylem. The diffusion

41

coefficients of the root tissues were inversely estimated by simulating the experiments at

42

night under the assumption that the convective fluxes were negligible. Inverse modelling

43

of the experiment at day gave the profile of water fluxes into the roots. For a 24 day-old

44

lupine grown in a soil with uniform water content, root water uptake was higher in the

45

proximal parts of lateral roots and it decreased toward the distal parts. The method allows

46

the quantification of the root properties and the regions of root water uptake along the root

47

systems.

48 49

Key words: Axial flux, Composite transport model, Convection-diffusion equation,

50

Deuterated water, Lupine, Neutron radiography, Radial flux, Root water uptake


51

Introduction

52

Understanding how and where plant roots extract water from soil remains an open

53

question for both plant and soil scientists. One of the open questions concerns the

54

locations of water uptake along the root system (Frensch and Steudle, 1989; Doussan et

55

al., 1998; Steudle, 2000; Zwieniecki et al., 2003; Javaux et al., 2008). Motivation of these

56

studies is that a better prediction of root water uptake may help to optimize irrigation and

57

identify optimal traits to capture water. Despite its importance, there is little experimental

58

information on the spatiotemporal distribution of the uptake zone along roots growing in

59

soil. The lack of experimental data is largely due to the technical difficulties in measuring

60

water fluxes in soils and roots.

61

Quantitative information of rate and location of root water uptake along roots growing in

62

soil is needed to better understanding the function of roots in extracting water from the

63

soil and tolerating drought events. Such information may show which parts of roots are

64

more involved in water extraction and how root hydraulic properties change during root

65

growth and exposure to water limiting conditions. For instance, it is not clear how root

66

anatomy and the hydraulic conductivity of roots change as the soil becomes dry or the

67

transpiration demand increases. Quantitative information of location of root water uptake

68

can be used to estimate the spatial distribution of hydraulic conductivities along roots.

69

This information is needed to parameterize the most recent and advanced models of root

70

water uptake, such as those of Doussan et al. (1998a) and Javaux et al. (2008).

71

Most of the experimental information on the spatial distribution of water uptake is limited

72

to roots grown in hydroponic and aeroponic cultures (Frensch and Steudle, 1989; Varney

73

and Canny, 1993; Zwieniecki et al., 2003; Knipfer and Fricke, 2010a). These

74

investigations substantially improved our knowledge of the mechanism of water transport

75

in roots. However, roots grown in hydroponic and aeroponic cultures may have different

76

properties than those of roots grown in soils. As the soil dries, the hydraulic conductivity

77

of roots and of the root-soil interface change and likely affect the profile of root water

78

uptake (Blizzard and Boyer, 1980; Nobel and Cui, 1992; Huang and Nobel, 1993;

79

McCully, 1995; North and Nobel, 1997; Carminati et al., 2011; Knipfer et al., 2011;

80

McLean et al., 2011; Carminati, 2012).


81

New advances in imaging techniques are opening new avenues for non-invasively

82

studying water uptake by roots in soils (Doussan et al., 1998; Garrigues et al., 2006;

83

Javaux et al., 2008; Pohlmeier et al., 2008; Moradi et al., 2011). Imaging methods such

84

as X-ray CT, light transmission imaging, nuclear magnetic resonance, and neutron

85

radiography allow quantifying the changes of water content in the root zone with different

86

accuracy and spatial resolution. However, due to the concomitant soil water

87

redistribution, the local changes in soil water content are not trivially related to root

88

uptake. Consequently, estimation of root water uptake requires coupling the imaging

89

methods with modeling of water flow in the soil, which, in turn, requires accurate

90

information on the hydraulic properties of soil and roots. An additional complexity is

91

represented by the peculiar and only partly understood hydraulic properties of the soil in

92

the vicinity of the roots, the so-called rhizosphere.

93

The hydraulic properties of the rhizosphere are influenced by root and microorganisms

94

activity, soil compaction due to root growth, and formation of air-filled gaps between soil

95

and roots when roots shrink (Nye, 1994; North and Nobel, 1997; Carminati et al., 2010;

96

Aravena et al., 2011; Moradi et al., 2011; Carminati, 2013; Zarebanadkouki and

97

Carminati, 2014). Up to date, it has been technically difficult to quantify the hydraulic

98

properties of the rhizosphere. Carminati et al. (2011) showed that the hydraulic properties

99

of the first 1-2 mm near root affect the profile of water content and water potential towards

100

the root.

101

Recently, we introduced a novel method to non-invasively trace the flow of water in soil

102

and roots (Zarebanadkouki et al., 2012; Zarebanadkouki et al., 2013). The method

103

combines neutron radiography and injection of deuterated water (D2O). Neutron

104

radiography is an imaging technique that allows to quantify the water distribution in thin

105

soil samples with high accuracy and spatial resolution (Moradi et al., 2008). D2O is an

106

isotope of normal water. Its chemical and physical properties are similar to those of H2O,

107

but in contrast to H2O, it is almost transparent in neutron transmission imaging

108

(Matsushima et al., 2012). This property makes D2O an excellent tracer for neutron

109

imaging of water flow.

110

In our former experiments (Zarebanadkouki et al., 2012; Zarebanadkouki et al., 2013),

111

D2O was injected next to selected roots and its transport was monitored using time-series


112

neutron radiography with a spatial resolution of 150 μm and a temporal resolution of 10

113

seconds for a duration of two hours. We grew lupines in aluminum containers (width of

114

25 cm, height of 30 cm, and thickness of 1 cm) filled with a sandy soil. The soil was

115

partitioned into different compartments with a 1 cm layer of coarse sand acting as

116

capillary barrier (3 vertical and 4 horizontal layers placed at regular intervals). The

117

capillary barriers limited the transport of D2O into a given region of soil and facilitated

118

the quantification of D2O transport into the roots. Figure 1 shows selected neutron

119

radiograph of D2O injection during day and nighttime. This figure is modified from

120

Zarebanadkouki et al. (2013). The radiographs showed that: 1) the radial transport of D2O

121

into the roots was faster during the day than during the nighttime measurement; and 2)

122

axial transport of D2O along the roots was visible only during daytime, while it was

123

negligible at nighttime measurement. The differences between night and daytime

124

measurements were caused by the net flow water induced by transpiration.

125

Interpretation of tracing experiments with D2O in which H2O and D2O are mixed is not

126

straightforward (Carminati and Zarebanadkouki, 2013; Warren et al., 2013a; Warren et

127

al., 2013b). To determine the convective fluxes from the radiographs, Zarebanadkouki et

128

al. (2012; 2013) introduced a diffusion-convection model of D2O transport in roots. The

129

model was solved analytically. The model described the increase of the average D2O

130

concentration in the root with a double-exponential equation, in which the rate constant

131

of the first and second phases were related to the transport of D2O into the cortex and the

132

stele of the roots. Although the model included important details of the root structure,

133

such as different pathways of water across the root tissue but the diffusion of D2O across

134

the root tissue was strongly simplified. In particular, our former model assumed that as

135

soon as the roots were immersed in D2O, the apoplastic free space of the root cortex

136

instantaneously saturated with D2O. In other words, we assumed that all cortical cells and

137

the root endodermis were simultaneously immersed in an identical concentration of D2O

138

equal to that of the soil. Additionally, we assumed that D2O concentration inside the

139

cortical cell, and the root stele was uniform (well stirred compartment).

140

Although the radiographs clearly showed a significant axial transport of D2O beyond the

141

capillary barrier during daytime (Fig. 1B), the model of Zarebanakouki et al. (2013) was

142

not capable of simulating it appropriately. Indeed, our former model could only simulate

143

the changes in D2O concentration in the root segments immersed in D2O. Since the 6 Downloaded from www.plantphysiol.org on September 7, 2014 - Published by www.plant.org Copyright © 2014 American Society of Plant Biologists. All rights reserved.

144

concentration of D2O in the root segment beyond the capillary barrier carry additional

145

information on the axial and radial fluxes along the roots, we decided to modify our model

146

to include such information.

147

Another approximation of the former model, was the assumption that the radial water

148

flow to root was uniform along the root segment immersed in D2O. However,

149

Zarebanadkouki et al. (2013) found significant variations in root water uptake along the

150

roots and suggested that root water uptake should be measured with a better spatial

151

resolution.

152

The objective of this study was to provide an adequate model to interpret tracing

153

experiments with D2O. We developed two different models to describe the transport of

154

D2O into roots:

155

1) In the first model we described the transport of D2O into the roots by taking into

156

account the different pathways of water across the root tissue: i.e. the apoplastic and the

157

cell-to-cell pathway. Although this model captures the complexity of the root structure, it

158

requires several parameters, such as the ratio of the water flow in the apoplast over the

159

water flow in the cell-to-cell pathway. We refer to this model as the “composite transport

160

model”.

161

2) In the second model we simplified the root tissue into a homogeneous flow domain

162

comprising both pathways. The latter model is a simplification of the complex root

163

anatomy, but it has the advantage of requiring less parameters. We refer to this model as

164

the “simplified model”.

165

In the next sections we introduce the two modelling approachs and we ran a sensitivity

166

analysis to test whether the transport of D2O into roots is sensitive to the parameters of

167

the composite transport model. The question was: do we need the composite transport

168

model to accurately estimate the water flow into the roots based on the experiments with

169

neutron radiography? Or alternatively, can we use the simplified model to estimate the

170

fluxes without the need of introducing several parameters?

171

Our final goal was to develop a numerical procedure to extract quantitative information

172

on the water fluxes and the root hydraulic properties based on the tracing experiments

173

with neutron radiography. We anticipate that, based on the results of the sensitivity


174

analysis, we chose the simplified model to simulate the experiments. By fitting the

175

observed D2O transport into the roots, we calculated the profiles of water flux across the

176

roots of a 24-days old lupine, as well as the diffusion permeability of its roots.

177 178

Theoretical background

179

Model of D2O transport in root

180

D2O enters the roots by 1) diffusion, which depends on the concentration gradient across

181

the root tissue and the diffusional permeability of the roots, and 2) by the convection

182

induced by the transpiration stream. The transport of D2O through the root can then be

183

described by a diffusion-convection model. We assumed that the water flow from the root

184

surface to the xylem surface is radial, while the water flow in the xylem is longitudinal

185

(Fig. 2a). Due to composite structure of roots, the radial flow of water and the transport

186

of D2O take place along different pathways: the apoplastic pathway and the cell-to-cell

187

pathway (Fig. 2c). The apoplastic pathway occurs along the cell walls and the

188

extracellular space. The cross-sectional area of the apoplastic pathway is only a few

189

percent of the total cross-sectional area – i.e. (Fritz and Ehwald, 2011) reported a value

190

of 3% in Maize. Although its cross section is small, the apoplastic pathway does not

191

involve crossing of cell membranes and it is expected to be less resistant to water flow.

192

However, the relative importance of the apoplastic and cell to cell pathways is still a

193

matter of debate (Steudle, 2000; Knipfer and Fricke, 2010b).

194

We chose two scenarios to describe the D2O transport in the root. In the first scenario, we

195

explicitly described the transport of D2O through the two different pathways and we

196

assumed that in the endodermis the apoplast is blocked. This assumption will not be valid

197

for the root tip that the endodermis is not yet developed. We will refer to this model as a

198

composite transport model. In the second scenario, we considered only a single pathway,

199

which can be seen as the average of the two pathways, and we described the endodermis

200

as a layer with lower diffusional permeability. We will refer to this model as simplified

201

model.

202

First scenario: composite transport model


203

We divided the flow domain into an apoplastic and a cell-to-cell pathway. A schematic

204

representation of the flow domain is shown in figure 2c. The pathways are in parallel and

205

exchange D2O with each other. We assumed a continuous apoplastic pathway across the

206

root tissue with an interruption at the endodermis, where the transport of D2O is only cell-

207

to-cell pathway. The transport of D2O in the apoplastic pathway is described by

208



209

and the transport of D2O in the cell to cell pathway is described by

210



211

where the superscripts a and c refers to the apoplastic and cell to cell pathway,

212

respectively, θ is the water content [cm3 cm-3], r is the radial coordinate [cm], x is the

213

longitudinal coordinate [cm], t is the time [s], ca and cc is the concentration of D2O in the

214

apoplastic and symplastic pathway, respectively [cm3 cm-3], Da and Dc is the diffusion

215

coefficient of D2O in the apoplastic and symplastic pathway, respectively [cm2 s-1], jx is

216

axial flux of water [cm s-1], 𝑗𝑟𝑎 and 𝑗𝑟𝑐 is radial flux of water in the apoplastic and

217

symplastic pathway, respectively [cm s-1], ωa is the volumetric fraction of the apoplast

218

[cm3 cm-3], and Γs describes the exchange of D2O between apoplastic and cell to cell

219

pathways [s-1]. The volumetric fraction of the apoplast, ωa, is assumed to be 3% (Richter

220

and Ehwald, 1983; Fritz and Ehwald, 2011). Note that we assumed a similar diffusion

221

coefficient in the radial and axial directions.

222

To quantify the exchange term, we followed the approach of Gerke and van Genuchten

223

(1996), who modeled water flow and solute transport in dual permeability soils. Although

224

their approach was developed for structured soils, the mathematical treatment can be

225

easily adapted to the root tissue. In fact, there is a strong analogy between the dualism

226

between macrospore and soil matrix in structured soils, and that of the apoplast and cell-

227

to-cell pathway in the root tissue. Using the approach of Gerke and van Genuchten (1996)

228

approach and assuming that root cells are cylinders with radius rc [cm], the exchange term

229

between apoplast and cell to cell pathway is given by:

c a   a c a     a c a    s  a a a  rD ( )  rj c  D ( )  j c        x  a t rr  r  rr r x  x  x  





cc   c cc     c cc    s  c c c  rD ( )  rj c     D ( )    jx c    a  r t rr  r  rr x  x  x  1  






(0)

(0)

Dc  1   a  ca  cc  rc 2

230

s 

231

where β is a dimensionless geometry coefficient, which was equal to 3 and 8 for a hollow

232

and a solid cylinder, respectively (van Genuchten, 1985; Gerke and van Genuchten,

233

1996). β is a parameter that depends on the ratio between the surface and volume of the

234

root cells. The larger is the surface to volume ratio, the faster is the D2O exchange between

235

the apoplast and the cell-to-cell pathway. We assumed that the cells have a cylindrical

236

shape – i.e. their radius is much smaller than their longitudinal length. We further assumed

237

that the major resistance to transport of D2O occurs at the cell membrane, while the inner

238

cell volume has a uniform concentration of D2O. These approximations result in the

239

representation of the root cells as hollow cylinders. The term “hollow” refers to the fact

240

the main resistance to D2O transfer acts at the cell wall.

241

We further assumed that the cell-to-cell pathway is in local hydraulic equilibrium with

242

the apoplast and that consequently D2O moves between the two pathways only by

243

diffusion.

244

The radial fluxes of water through the apoplastic and cell-to-cell pathways are expressed

245

as

246 247 248

j ra 

(0)

1    jr

(0)

a

and

j rc 

 jr c

(0)

249

where jr is the average radial flux of water [cm s-1], λ is the relative importance of the

250

apoplastic transport [-] and ωc is the volumetric fraction of the cell to cell pathway (1-

251

ωa). The value of λ varies from zero for purely apoplastic transport to one for purely cell-

252

to-cell transport. Note that the radial and axial fluxes vary as a function of distance from

253

the root center (radial direction r) and from the root tip (axial direction x). The fluxes are

254

assumed to be constant over time during the measurements. We define jR(x) as the radial

255

flux at the root surface [cm s-1].


256

The change in concentration of D2O in the root can be calculated from the weighted-

257

average concentrations of D2O in the apoplastic and cell-to-cell pathway according to

258

cr c a c c  a  c t t t

259

where cr is the D2O concentration in the root [cm3 cm-3].

260

Mass-conservation imposes that the radial and axial fluxes satisfy the following equation:

261

 rx2

262

where rx is the xylem radius [cm]. From the root surface to the root xylem, we assumed

263

only radial flow. In another words, we assumed that the axial transport of water occurs

264

only in the xylem. In this case, mass conservation imposes that 𝑗𝑟 × 𝑟 is constant between

265

the root surface and the xylem radius.

266

Second scenario: simplified model

267

A simplified approach consists in treating the root tissue as a single pathway, whose

268

diffusion D is an average of the diffusion through the apoplast and cell-to-cell pathway

269

[cm2 s-1]. A schematic representation of the model is presented in figure 2d. In this case,

270

the transport of D2O in root can be described by

271



272

here cr is the average concentration of D2O in root.

273

Model parameterization

274

All the variables in Eq. 1, Eq. 2 and Eq. 8 are function of the radial and longitudinal

275

coordinates (r, x). For the diffusion coefficients, we assumed that the cortical cells in the

276

cortex and the root stele had constant radius and diffusion coefficient along r and x. We

277

further assumed that the endodermis was not yet developed in the first 1.5 cm from the

278

root tip. Thus, we used the diffusion coefficient in the root tip as a representative of

279

diffusion coefficient of the cortical cells in the root tissue. We let the diffusion coefficient

jx  x  x

(0)

 2 rx jr  rx , x 

(0)

cr cr   c      )   rjr cr    D ( r )    jxcr   rD ( t rr  r  rr x  x  x

(0)


280

of the endodermis (De) and the radial flux of water into the roots vary with x – i.e

281

De=De(x) and jR=jR(x).

282

For the composite transport model we assumed that the volume fractions of the apoplastic

283

and cell-to-cell pathways are ωa and (1- ωa), respectively. Similarly, the fraction of the

284

water flow through the apoplast and the through the cell-to-cell pathway is 1- λ and λ,

285

respectively. As a first approximation, we assumed that ωa and λ are constant in the axial

286

direction. The apoplastic pathway is assumed to be interrupted at the endodermis – i.e.

287

between 𝑟𝑒 −

288

also included the fact the diffusion in the endodermis is smaller than in the cortex. These

289

assumptions are summarized as:

𝑟𝑐 2

𝑟

and 𝑟𝑒 + 𝑐, with rc being the cell radius and re the endodermis radius. We 2

290

291

 D c  r , x   De  x  r r  For r  [re  c : re  c ]    r , x   1 2 2  a    r, x   0

292

Note that when ωa(r,x)=0, Eq. (1) cannot be solved. Indeed, in the endodermis we solved

293

only Eq. (2).To solve the numerical problem we imposed Ca= Cc in the endodermis.

294

For simplicity, we did not simulate the water movement in soil during D2O injection. The

295

radiographs showed a quick water redistribution in the soil after D2O injection, and we

296

assumed that afterwards the water flow in soil was constant over time. During D2O

297

injection, we imposed the measured concentration of D2O as the boundary condition at

298

the root surface in soil. When the soil water content reached equilibrium, we shifted the

299

boundary condition to the last node of the soil and we simulated D2O diffusion through

300

the soil. The diffusion coefficient in soil was parameterized according to Millington and

301

Quirk (1961):

302

  7/3  D   D0  2   

(0)

(0)

303


304

where θ is the soil water content [cm3 cm-3], D0 is the diffusion coefficient of D2O in pure

305

water [cm2 s-1], and ϕ is the soil porosity. We used D0 = 2.27 × 10-9 m2 s-1, as measured

306

by (Longsworth, 1960).

307

The diffusion coefficients of the root tissue were defined as following: the diffusion of

308

D2O in the apoplastic pathway was assumed to be one sixth of the diffusion coefficients

309

of D2O in pure water (D0= 2.27×10-9 m2 s-1). Published values of diffusion coefficients

310

for different solutes in the apoplast range from 1/5 to 1/ 60 of the diffusion in pure water

311

(Pitman, 1965; Aikman et al., 1980; Richter and Ehwald, 1983; Kramer et al., 2007). We

312

took the lower limit because D2O is a neutral molecule with a rather similar molecular

313

weight compared to normal water. Higher values are expected for bigger and charged

314

molecules. We assumed the same value for the diffusion in the xylem.

315

The diffusion coefficients of cortex and endodermis were obtained from inversely fitting

316

the D2O distribution in roots during nighttime. We fitted the D2O transport in the tip root

317

segments assuming a constant diffusion coefficient across root tissue. This coefficient

318

was used for the cortical cells in the root cortex and the root stele along root length and

319

root radius. Then, we fitted the D2O transport in the rest of the root segments to calculate

320

the diffusion coefficient of the endodermis assuming a constant diffusion coefficient for

321

the cortical cells obtained from the root tip.

322

We used the fitted diffusion coefficients for simulating the daytime experiments. For the

323

daytime simulations the parameters to fit were jR(x), λ and β for the composite transport

324

model, and jR(x) for the simplified model. For those roots that were partly immersed in

325

D2O we also fitted the axial flux of water entering into the root segment immersed in

326

D2O. Note that as a first attempt, we assumed that λ and β are uniform along the root

327

length. This assumption may not be valid at the root tip, where the endodermis is not yet

328

developed and water may flow mainly through apoplast. The radial fluxes and diffusion

329

coefficients are fitted for each longitudinal position along a root with intervals of 0.1 cm.

330

Model implementation

331

A single root and the surrounding soil were modeled in cylindrical coordinates. To

332

numerically solve Eq. 7 and Eq. 8, each variable was represented in a 2D matrix. Each

333

element of the matrix encodes the identity of a specific portion of the root in radial and


334

longitudinal position. In our model, the soil was extended for one centimeter from the

335

root surface. The root cortex extended from the root surface to the endodermis. The stele

336

extended from the inner radius of the endodermis to the surface of xylem. We described

337

the xylem as a single cylinder with a cross sectional area corresponding to the total cross

338

sectional area of xylem vessels. The radius of the root, of the endodermis, of the cortical

339

cells and the cross sectional area of xylem was calculated from microscopic observation

340

of the root cross-section (fig. 2C).

341

Eq. 7 and Eq. 8 were solved numerically using a centered finite difference method. We

342

used a rectangular computational grid with N equally spaced grid elements along the root

343

radius and M grid elements along the root length. The space discretization along root

344

length and root radius was 0.1 cm and 0.0006 cm, respectively. The time derivatives were

345

discretized with an explicit method. To assure stability of the simulations we used a time

346

step of 10-3 seconds.

347

The inverse problem was solved with a linear least squares method using the lsqlin solver

348

in Matlab. The lsqlin solver is based on the Levenberg-Marquardt algorithm, which starts

349

by searching the minimum along the steepest gradient of the objective function and

350

gradually switches to a direction based on a first-order approximation of the objective

351

function. The objective function to minimize was the difference between measured and

352

simulated concentration of D2O along the root over time.

353

Different objective functions were used to estimate different parameters of the model. We

354

used the difference between measured and simulated concentration of D2O along a root

355

at different times as objective function to estimate De(x) and jR(x). When the root was

356

partly immersed in D2O, to estimate the axial flux of normal water coming to the root

357

segment immersed in D2O, the objective function was the difference between the average

358

measured and simulated concentration of D2O in the root segment immersed in D2O. Note

359

that the final concentration of D2O in the root segment immersed in D2O depends on the

360

axial flux of normal water coming into the root segment immersed in D2O. The difference

361

between average measured and simulated concentration of D2O in the root segment

362

beyond the capillary barrier was used as the objective function to estimate λ.

363

We run a sensitivity analysis to understand whether the composite transport model was

364

sensitive to the parameters λ and β. To this end, as a first step, we fitted the increase of 14 Downloaded from www.plantphysiol.org on September 7, 2014 - Published by www.plant.org Copyright © 2014 American Society of Plant Biologists. All rights reserved.

365

D2O concentration into 15 roots during nighttime. After solving the inverse problem, we

366

obtained the distribution of the diffusion coefficients along the root length. We used these

367

diffusion coefficients to simulate the transport of D2O in the root for varying parameters

368

JR, λ and β. The objective of the sensitivity analysis was to understand if the composite

369

transport model is needed or, else, if the simplified model can replace it without loss of

370

precision.

371

Results

372

We first show the results of the sensitivity analysis. Figure 3 shows the simulated

373

concentrations of D2O in a root segment immersed in D2O (Fig. 3A) and in the next root

374

segment beyond the capillary barrier (Fig. 3B). We chose a range of reasonable values

375

for jR and β, and we let λ vary from the minimum value of zero to the maximum value of

376

1. For the sensitivity analysis, we assumed that jR was constant along x.

377

The results show that the increase of D2O inside the root immersed in D2O was affected

378

by the radial flux jR. Note that in figure 3 and in all the next figures, jR refers to the water

379

fluxes at the root surface. When jR =0, the increase of D2O was driven by diffusion and

380

was visibly slower. The increase of D2O was faster as jR increased. Almost no differences

381

were observed in the average concentration of D2O in the root segment immersed in D2O

382

when the water flow changed from purely apoplastic (λ=0) to purely cell-to-cell pathway

383

(λ=1). Similarly, the concentrations of D2O in the root segment immersed in D2O were

384

not sensitive to β. We varied β from a value of 3 to 8, corresponding to a hollow cylinder

385

and a solid cylinder, respectively (van Genuchten, 1985; Gerke and van Genuchten,

386

1996).

387

When the radial flux increased by a factor of five, D2O concentration beyond the capillary

388

barrier equilibrated to a lower value (Fig. 3B). The time needed to reach equilibrium was

389

faster. This observation is explained by the convective radial fluxes into the root that

390

opposes to the diffusion of D2O from xylem to the rest of root tissue. In other words, the

391

higher are the convective fluxes, the lower is the equilibrium concentration of D2O

392

beyond the capillary barrier. The pathway of water through the tissue plays a role in this

393

process: if the main pathway is cell-to-cell (λ=1), the convective transport efficiently

394

limits the diffusion; instead, if the main pathway is apoplastic (λ=0), the convective fluxes

395

bypass the root cells and are less efficient in opposing to the diffusion of D2O out of the 15 Downloaded from www.plantphysiol.org on September 7, 2014 - Published by www.plant.org Copyright © 2014 American Society of Plant Biologists. All rights reserved.

396

xylem. This is visible in figure 3B, where the equilibrium value of the D2O concentration

397

was lower for λ=1 than for λ=0. However, for the used diffusion coefficients and root

398

radius, the differences between the simulations with λ=1 and with λ=0 probably lie within

399

our measurement errors. The same conclusion holds for β.

400

This sensitivity analysis showed that the composite transport is not sufficiently sensitive

401

to the pathways of water through the root tissue. Therefore, to reduce the numbers of

402

unknown parameters, we used the simplified model to quantify the transport of D2O into

403

roots.

404

Figure 4 shows the diffusion coefficients of the endodermis as a function of distance from

405

the root tip De(x). The data are obtained from the best fit of the simplified model to the

406

observed average D2O concentration of 15 roots measured at nighttime. Figure 4 shows

407

that De(x) was higher in the distal root segments and it decreased 10 times towards the

408

proximal segment.

409

We used the diffusion coefficients estimated from the night measurements to simulate the

410

transport of D2O into the roots during the day. The parameter to be fitted for the day

411

measurements was jR(x). We let jR(x) free to change along the roots and we inversely

412

estimated it by finding the best-fit of the simplified model to the observed average D2O

413

concentration in roots measured at daytime. The simulated two-dimensional distribution

414

of the D2O concentration in a root of 14 cm at different time steps after D2O injection is

415

shown in figure 5. The images show that as D2O reached the xylem, it was transported

416

axially along the root and then it diffused back in the segment beyond the barrier that was

417

immersed in H2O.

418

Figure 6 shows a comparison between the simulations shown in figure 5 and the

419

experimental data obtained from neutron radiographs. The location of D2O injection is

420

illustrated in figure 7A. The average concentrations of D2O in the root segment immersed

421

in D2O (Fig. 6A) and in the root segment beyond the capillary barrier (Fig. 6B) showed a

422

good agreement with the experimental data.

423

We fitted the profiles of D2O concentration along six roots during daytime. We selected

424

roots that had a similar root length and were located at similar soil depth. Root lengths

425

and location of D2O injection are shown in figure 7. We chose three roots that were partly


426

immersed in D2O at their middle parts (Fig. 7A) and three roots that were partly immersed

427

in D2O at their proximal parts (Fig. 7B). The fitted radial fluxes along the six roots are

428

plotted in figure 8. The results show that water uptake along the lateral roots was not

429

uniform. Water flux was higher in the proximal segments and it decreased towards the

430

distal segments. Remarkably, the radial fluxes predicated for the root segmented beyond

431

the capillary barrier for the roots that were immersed in D2O at the middle parts (Fig. 7A)

432

were in line with the flux predicted for the roots that were immersed in D2O at the

433

proximal parts (Fig. 7B) – i.e. compare the open and solid symbols at distance of 10-16

434

cm from the root tip in figure 8. This agreement shows the validity of our method in

435

estimating the radial fluxes for the root segment immersed in D2O and the root segment

436

beyond the capillary barrier.

437

Additionally, the profile of jR(x) along the root was in agreement with the results of

438

Zarebanadkouki et al. (2013). In figure 8, we compared the results of Zarebanadkouki et

439

al. (2013) with those of the new model. In Zarebanadkouki et al (2013) the radial fluxes

440

were calculated for the radius of the endodermis. Here they have been scaled for being

441

comparable to jR(x). The results of the two models match well.

442

Discussion

443

We have implemented a new model of D2O transport in the roots to quantify the water

444

fluxes from the neutron radiographs. The model describes the transport of D2O with a

445

diffusion-convection equation in cylindrical coordinates, and it includes different

446

pathways: the apoplastic pathway and the cell-to-cell pathway.

447

A sensitivity analysis indicated that the transport of D2O was not sensitive to the

448

parameter λ, which describes the relative importance of the apoplastic and cell-to-cell

449

pathways. Therefore, to reduce the number of parameters, we used a simplified model in

450

which there is only one lumped pathway of water across the root tissue. The model was

451

sensitive to both the diffusional coefficient of D2O across the root tissue and to the radial

452

water flux into the root. Fitting for the diffusion coefficient the nighttime measurements

453

and using the same coefficients for the daytime measurements allowed us to calculate the

454

radial flux of water into the root as a function of distance from the root tip. The results

455

showed that the diffusion coefficient was higher near the root tip and it decreased towards

456

the proximal parts. The diffusion coefficient of the tip root was 6.7×10-11 m2 s-1 and it 17 Downloaded from www.plantphysiol.org on September 7, 2014 - Published by www.plant.org Copyright © 2014 American Society of Plant Biologists. All rights reserved.

457

decreased to 6.5×10-12 m2 s-1 at a distance of 14 cm from the root tip. Oppositely, the

458

radial flux of water was lower in the distal segments than in the proximal segments. It

459

was 3×10-8 m s-1 at a distance of 6 cm from the root tip and it increased to 1.6×10-7 m s-1

460

at a distance of 15 cm from the root tip. The results are in agreement with those obtained

461

with the former model of Zarebanadkouki et al. (2013) (fig. 8).

462

The sensitivity analysis showed that the D2O transport was not sensitive to the pathways

463

of water across the root tissue. The low sensitivity of the model was caused by the

464

significant contribution of diffusion to the movement of D2O into root. However, our

465

sensitivity analysis is limited to the special case studied here and cannot be generalized

466

to all roots. For example, the pathways of water may become important for thicker roots

467

with low diffusion coefficients, in which convection is likely to become more important

468

than diffusion. Some sensitivity was observed for the root segment after the barrier – i.e.

469

in the segments after the region immersed in D2O (Fig. 3B). If the sensitivity increases

470

and the error in our measurements decreases thanks to future technical improvements, it

471

may become possible to estimate the relative importance of the pathways.

472

Another issue is that our sensitivity analysis is constrained to our assumptions. One of

473

our assumptions is that the apoplastic pathway was completely blocked by the

474

endodermis. In case the endodermis did not fully block the apoplast, our model should

475

become more sensitive to λ. We also assumed that the diffusion coefficient of the cortical

476

cells was constant along the roots. However, as roots get older, their cell membrane

477

becomes less permeable (Bramley et al., 2009). This overestimation of the diffusion

478

coefficient of the cortical cells in the proximal root segments would result in a quick

479

equilibrium between the D2O concentrations in the apoplastic and cell-to-cell pathways.

480

In this case, the concentration of D2O in the root is independent from the pathways of

481

water, due to the similar concentration of D2O in both pathways.

482

The advantage of our new model compared to the previous version is that it fully solves

483

the diffusion and convection of D2O in both radial and axial directions. In the previous

484

model, D2O diffusion was strongly simplified. There, we assumed an immediate transport

485

of D2O through the apoplast. We also assumed that the concentration of D2O in the root

486

stele (45 percent of root volume) was uniform. In our new model, we explicitly solved


487

the diffusion from the root surface to the xylem, including the endodermis as a layer with

488

reduced diffusion coefficient.

489

Our new model includes the back diffusion of normal water from the xylem to the rest of

490

the tissue. The back diffusion of D2O from the xylem to the rest of the root tissue becomes

491

significant when roots are partly immersed in D2O. In this case, normal water is

492

transported into the segments of the xylem immersed in D2O. This normal water will

493

diffuse through the root tissue and the D2O concentration in the root will not converge to

494

the concentration of D2O in soil. Additionally, in our new model the axial transport of

495

D2O is fully solved. This allows estimating the profile of radial flux along the root length

496

with a higher spatial resolution compared to the previous model. The previous model

497

estimated the fluxes based on the average concentration of D2O in the root segment

498

immersed in D2O and had a spatial resolution of around 5 cm.

499

To calculate jR(x) we assumed that the diffusion coefficient of cortical cells and

500

endodermis was constant during day and night. Although this choice allows to reduce the

501

uncertainty in the parameter estimation, the validity of this assumption should be critically

502

discussed. In fact, changes in aquaporin’s activity in response to variations in the

503

transpiration demand may alter the diffusion of D2O through the cell-to-cell pathway, the

504

exchange of D2O between apoplast and cell-to-cell pathway, and the fraction of water

505

flow through the cell-to-cell pathway λ. In case of an increased aquaporin activity during

506

day and a consequent increase in the diffusion coefficients, our approach would result in

507

an overestimation of jR(x). This is probably the most critical problem of our approach and

508

it is our priority to properly address it.

509

Our method and assumptions could be improved by three-dimensional imaging of D2O

510

transport in root. A three-dimensional profile of D2O concentration in roots might open

511

new possibilities to estimate the relative importance of the apoplastic to cell-to-cell

512

pathways. In our study, we derived the average concentration of D2O across roots from

513

two-dimensional radiography and the model was employed to best fit the average

514

concentration. However, an average concentration of D2O in the root is obviously not

515

sufficient to estimate the spatial distribution of D2O across the root tissue.

516

advancements in neutron tomography imaging could also allow quantifying the diffusion

517

coefficient of cortical cells along the root. To this end, tomography faster than one minute


New

518

would be required. While waiting for future advancements in neutron imaging, we can

519

use our modeling approach to reconstruct the water transport through the entire root

520

systems.

521

In conclusion, the significance of this study is the description of a new method to locally

522

quantify flow of water into living roots grown in soil. Thanks to this method we can

523

measure where do roots take up water from soil. So far, we employed the method to study

524

lupines growing in sandy, wet soils. As the soil dries, the hydraulic conductivity of roots

525

and their rhizosphere is expected to decrease, affecting root water uptake. In these

526

circumstances, the location of root water uptake may shift to different root segments, for

527

instance to young and distal root segments covered with hydrated mucilage, as proposed

528

by Carminati and Vetterlein (2013). This method would allow testing such hypothesis.

529

It would be also of high interest to employ the method to study water uptake in plants

530

with contrasting root architectures and growing in different soil conditions. The measured

531

water fluxes into the roots can be used to reconstruct the profile of axial and radial

532

hydraulic conductivities as well as the xylem water potential along the root system, as

533

done in Doussan et al. (1998b). Such information will hopefully help to identify the root

534

traits that best increase the plant efficiency in taking up water from soil.

535

Materials and methods

536

Experimental Set-up

537

Soil and plant preparation and image processing are described in details in

538

Zarebanadkouki et al. (2012; 2013). Lupines were grown in 25 cm wide, 30 cm high and

539

1 cm thick aluminum containers filled with a sandy soil. The soil was partitioned into 16

540

compartments using 1 cm layers of coarse sand as capillary barriers, which served to limit

541

the diffusion of D2O in selected regions (fig. 9). The measurements with neutron

542

radiography were conducted when plants were 18–21 days old. The plants were regularly

543

irrigated during growth. The soil water content in each compartment ranged from 0.10 to

544

0.20 cm3 cm-3 at the beginning of the neutron radiography experiment. We injected D2O

545

in selected soil regions and its transport into the roots was monitored for 2 hours using

546

time-series neutron radiography at the imaging station ICON at the Paul Scherrer Institute

547

(PSI), Switzerland. The measurements were performed during daytime when plants fully

548

transpired and nighttime when transpiration was reduced. The sharp contrast between 20 Downloaded from www.plantphysiol.org on September 7, 2014 - Published by www.plant.org Copyright © 2014 American Society of Plant Biologists. All rights reserved.

549

roots and the surrounding soil allowed us to distinguish and segment the roots from the

550

soil. The segmented roots were skeletonized and their lengths and diameters were

551

calculated using the Euclidean distance. Neutron attenuation in the pixels containing roots

552

was the sum of the attenuation coefficients of the roots and of the soil in front of and

553

behind the roots in the beam direction (across soil thickness). The actual contributions of

554

H2O and D2O in the roots were calculated assuming that the amounts of H2O and D2O in

555

the soil in the front of, and the behind of the roots were equal to those of the soil at the

556

sides of the roots. We calculated the volumetric concentration of D2O in roots (Cr) and

557

soil (C0) as the thickness of D2O divided by the total liquid thickness in roots and soil,

558

respectively. More details about the image processing are found in Zarebanadkouki et al.

559

(2012).


560 561

Acknowledgements

562

Our acknowledgments go to Jan Vanderborght, Katrin Huber and Heino Nietfeld for

563

their discussions and suggestions on the composite transport model. We thank Valentin

564

Couvreur and Chris Topp for the helpful suggestions and comments on a previous

565

version of this manuscript.


566

Appendix

567

θ is the water content [cm3 cm-3] in corresponding medium (soil or root tissue)

568

r is the radial coordinate [cm],

569

rc is the radius of cortical cells [cm]

570

rx is the xylem radius [cm]

571

re is the radius of endodermis [cm]

572

x is the longitudinal coordinate [cm]

573

t is the time starting from arrival of D2O at the root surface [s],

574

ca is the concentration of D2O in the apoplastic [cm3 cm-3]

575

cc is the concentration of D2O in the symplastic pathway [cm3 cm-3]

576

cr is the concentration of D2O in the root [cm3 cm-3]

577

Da is the diffusion coefficient of D2O in the apoplastic pathway [cm2 s-1]

578

Dc is the diffusion coefficient of D2O in the symplastic pathway [cm2 s-1]

579

D is the diffusion coefficient of D2O in the root assuming that the root is a uniform tissue

580

[cm2 s-1]

581

D0 is the diffusion coefficient of D2O in pure water [cm2 s-1]

582

De is the diffusion coefficient of D2O across the endodermis [cm2 s-1]

583

jx is axial flux of water [cm s-1]

584

𝑗𝑟𝑎 is radial flux of water in the apoplastic pathway calculated for the radius of root [cm s-

585

1

586

𝑗𝑟𝑐 is radial flux of water in the symplastic pathway calculated for the radius of root [cm

587

s-1]

588

jr is the radial flux of water in the root [cm s-1]

589

jR is the radial flux of water at the root surface [cm s-1]

590

ωa is the volumetric fraction of the apoplast [cm3 cm-3]

591

ωc is the volumetric fraction of the cell to cell pathway (1-ωa).

592

Γs the exchange term of D2O between apoplastic and cell to cell pathways [s-1].

593

λ is the fraction of water flow through the cell-to-cell pathway [-]

594

β is a dimensionless geometry coefficient, which was equal to 3 and 8 for a hollow and a

595

solid cylinder, respectively

596

ϕ is the soil porosity [cm3 cm-3]

]


597

References

598 599

Aikman DP, Harmer R, Rust TSO (1980) Electrical resistance and ion movement through excised discs of sugar beet root tissue. Physiol Plant 48: 395–402

600 601 602

Aravena JE, Berli M, Ghezzehei TA, Tyler SW (2011) Effects of Root-Induced Compaction on Rhizosphere Hydraulic Properties - X-ray Microtomography Imaging and Numerical Simulations. Environ Sci Technol 45: 425–431

603 604

Blizzard WE, Boyer JS (1980) Comparative resistance of the soil and the plant to water transport. Plant Physiol 66: 809–814

605 606 607

Bramley H, Turner NC, Turner DW, Tyerman SD (2009) Roles of Morphology, Anatomy, and Aquaporins in Determining Contrasting Hydraulic Behavior of Roots. Plant Physiol 150: 348–364

608 609

Carminati A (2012) A Model of Root Water Uptake Coupled with Rhizosphere Dynamics. Vadose Zone J 11: 0. doi:10.2136/vzj2011.0106.

610 611 612

Carminati A (2013) Rhizosphere wettability decreases with root age: a problem or a strategy to increase water uptake of young roots? Front Plant Sci. doi: 10.3389/fpls.2013.00298

613 614 615

Carminati A, Moradi AB, Vetterlein D, Vontobel P, Lehmann E, Weller U, Vogel H-J, Oswald SE (2010) Dynamics of soil water content in the rhizosphere. Plant Soil 332: 163–176

616 617 618

Carminati A, Schneider CL, Moradi AB, Zarebanadkouki M, Vetterlein D, Vogel H-J, Hildebrandt A, Weller U, Schüler L, Oswald SE (2011) How the Rhizosphere May Favor Water Availability to Roots. Vadose Zone J 10: 988

619 620

Carminati A, Vetterlein D (2013) Plasticity of rhizosphere hydraulic properties as a key for efficient utilization of scarce resources. Ann Bot 112: 277–290

621 622

Carminati A, Zarebanadkouki M (2013) Comment on: “neutron imaging reveals internal plant water dynamics.”Plant Soil 369: 25–27

623 624 625

Doussan C, Pagès L, Vercambre G (1998) Modelling of the hydraulic architecture of root systems: an integrated approach to water absorption—model description. Ann Bot 81: 213–223

626 627

Frensch J, Steudle E (1989) Axial and radial hydraulic resistance to roots of maize (Zea mays L.). Plant Physiol 91: 719–726

628 629

Fritz M, Ehwald R (2011) Mannitol permeation and radial flow of water in maize roots. New Phytol 189: 210–217


630 631 632

Garrigues E, Doussan C, Pierret A (2006) Water Uptake by Plant Roots: I – Formation and Propagation of a Water Extraction Front in Mature Root Systems as Evidenced by 2D Light Transmission Imaging. Plant Soil 283: 83–98

633 634

Van Genuchten MT (1985) A general approach for modeling solute transport in structured soils. Mem Int Assoc Hydrogeol 17: 513–526

635 636 637

Gerke HH, van Genuchten MT (1996) Macroscopic representation of structural geometry for simulating water and solute movement in dual-porosity media. Adv Water Resour 19: 343–357

638 639

Huang B, Nobel PS (1993) Hydraulic conductivity and anatomy along lateral roots of cacti: changes with soil water status. New Phytol 123: 499–507

640 641 642

Javaux M, Schröder T, Vanderborght J, Vereecken H (2008) Use of a ThreeDimensional Detailed Modeling Approach for Predicting Root Water Uptake. Vadose Zone J 7: 1079

643 644

Knipfer T, Besse M, Verdeil J-L, Fricke W (2011) Aquaporin-facilitated water uptake in barley (Hordeum vulgare L.) roots. J Exp Bot 62: 4115–4126

645 646

Knipfer T, Fricke W (2010a) Water uptake by seminal and adventitious roots in relation to whole-plant water flow in barley (Hordeum vulgare L.). J Exp Bot 62: 717–733

647 648 649

Knipfer T, Fricke W (2010b) Root pressure and a solute reflection coefficient close to unity exclude a purely apoplastic pathway of radial water transport in barley (Hordeum vulgare). New Phytol 187: 159–170

650 651

Kramer EM, Frazer NL, Baskin TI (2007) Measurement of diffusion within the cell wall in living roots of Arabidopsis thaliana. J Exp Bot 58: 3005–3015

652 653

Longsworth LG (1960) The mutual diffusion of light and heavy water. J Phys Chem 64: 1914–1917

654 655 656

Matsushima U, Kardjilov N, Hilger A, Graf W, Herppich WB (2012) Application potential of cold neutron radiography in plant science research. J Appl Bot Food Qual 82: 90–98

657 658

McCully M (1995) How Do Real Roots Work?(Some New Views of Root Structure). Plant Physiol 109: 1-6

659 660 661

McLean EH, Ludwig M, Grierson PF (2011) Root hydraulic conductance and aquaporin abundance respond rapidly to partial root-zone drying events in a riparian Melaleuca species. New Phytol 192: 664–675

662 663

Millington RJ, Quirk JP (1961) Permeability of porous solids. Trans Faraday Soc 57: 1200–1207


664 665 666

Moradi AB, Carminati A, Vetterlein D, Vontobel P, Lehmann E, Weller U, Hopmans JW, Vogel H-J, Oswald SE (2011) Three-dimensional visualization and quantification of water content in the rhizosphere. New Phytol 192: 653–663

667 668 669

Moradi AB, Conesa HM, Robinson B, Lehmann E, Kuehne G, Kaestner A, Oswald S, Schulin R (2008) Neutron radiography as a tool for revealing root development in soil: capabilities and limitations. Plant Soil 318: 243–255

670 671

Nobel PS, Cui M (1992) Hydraulic conductances of the soil, the root-soil air gap, and the root: changes for desert succulents in drying soil. J Exp Bot 43: 319–326

672 673 674

North GB, Nobel PS (1997) Drought-induced changes in soil contact and hydraulic conductivity for roots of Opuntia ficus-indica with and without rhizosheaths. Plant Soil 191: 249–258

675 676

Nye PH (1994) The effect of root shrinkage on soil water inflow. Philos Trans R Soc Lond B Biol Sci 345: 395–402

677 678

Pitman M (1965) Sodium and Potassium Uptake by Seedlings of Hordeum Vulgare. Aust J Biol Sci 18: 10–24

679 680 681 682

Pohlmeier A, Oros-Peusquens A, Javaux M, Menzel MI, Vanderborght J, Kaffanke J, Romanzetti S, Lindenmair J, Vereecken H, Shah NJ (2008) Changes in Soil Water Content Resulting from Root Uptake Monitored by Magnetic Resonance Imaging. Vadose Zone J 7: 1010-1017

683 684

Richter E, Ehwald R (1983) Apoplastic mobility of sucrose in storage parenchyma of sugar beet. Physiol Plant 58: 263–268

685 686

Steudle E (2000) Water uptake by plant roots: an integration of views. Plant Soil 226: 45–56

687 688

Varney GT, Canny MJ (1993) Rates of water uptake into the mature root system of maize plants. New Phytol 775–786

689 690

Warren JM, Bilheux H, Cheng C-L, Perfect E (2013a) Reply to: Comment on “neutron imaging reveals internal plant water dynamics.”Plant Soil 371: 15–17

691 692

Warren JM, Bilheux H, Kang M, Voisin S, Cheng C-L, Horita J, Perfect E (2013b) Neutron imaging reveals internal plant water dynamics. Plant Soil 366: 683–693

693 694

Zarebanadkouki M, Carminati A (2014) Reduced root water uptake after drying and rewetting. J Plant Nutr Soil Sci 177: 227–236

695 696 697

Zarebanadkouki M, Kim YX, Carminati A (2013) Where do roots take up water? Neutron radiography of water flow into the roots of transpiring plants growing in soil. New Phytol 199: 1034-1044

698 699

Zarebanadkouki M, Kim YX, Moradi AB, Vogel H-J, Kaestner A, Carminati A (2012) Quantification and Modeling of Local Root Water Uptake Using Neutron


700 701 702 703 704

Radiography and Deuterated doi:10.2136/vzj2011.0196

Water.

Vadose

Zone

J

11:

Zwieniecki MA, Thompson MV, Holbrook NM (2003) Understanding the Hydraulics of Porous Pipes: Tradeoffs Between Water Uptake and Root Length Utilization. J Plant Growth Regul 21: 315–323

705


706

List of figures

707

Figure 1: Neutron radiographs of two samples after injection of 4 ml D2O during day (A

708

and B) and during night (C and D). D2O was injected in one compartment during

709

nighttime and in two compartments during daytime. The images are the differences

710

between the actual radiographs at time t and the radiograph before injection (t=0).

711

Brighter colors indicate lower neutron attenuation and higher D2O/H2O ratio. The images

712

show that: 1) the transport of D2O was faster during day than during night; 2) D2O moved

713

axially beyond the capillary barrier towards the shoot only during day. Images are close-

714

up of the original field of view of 15.75×15.75 cm showing the distribution of D2O in the

715

soil and root after D2O injection. Figures are extracted from Zarebanadkouki et al. 2013.

716

(A neutron radiograph of the whole sample used for daytime measurement is given in

717

figure 9).

718

Figure 2. Illustration of D2O transport into a root partially immersed in D2O. A) Diffusion

719

and convection along a root. Water flows radially till the xylem radius. In the xylem,

720

water flows longitudinally. B) Cross section of a lupine root at a distance of 12 cm from

721

the root tip C) Representation of the root tissue and its effect on D2O transport in the

722

composite transport model. D) Simplified model in which the different pathways are

723

lumped together in a single averaged pathway across the root tissue. Here, ca and cc are

724

the concentration of D2O in the apoplastic and the symplastic pathway, respectively, cr

725

is the concentration of D2O in the root, Da and Dc are the diffusion coefficient of D2O in

726

the apoplastic pathway and the symplastic pathway, respectively, D is the diffusion

727

coefficient of D2O in the root assuming root as a uniform tissue, jar and jcr are radial flux

728

of water in the apoplastic pathway and the symplastic pathway, respectively, jr is the

729

radial flux of water into the root and Γs the exchange term of D2O between apoplastic and

730

cell to cell pathways.

731

Figure 3. Sensitivity analysis of the composite transport model. Average concentration of

732

D2O in the root segment immersed in D2O (Fig. 3A) and in the root segment beyond the

733

capillary barrier (Fig. 3B).

734

Figure 4. Diffusion coefficient of the obtained from the best fit of the simplified model to

735

the experimental data of D2O concentration across the root tissue at nighttime. Note that


736

we assumed that in the first 1.5 cm near the root tip the diffusion of the endodermis is

737

equal to that of the cortex. The data are obtained from 15 roots.

738

Figure 5. Simulated concentration of D2O across the root tissue at different times after

739

D2O injection. The color bar shows the concentration of D2O in the root. The length of

740

the root and the location of D2O injection is presented in figure 7A.Figure 6. Measured

741

concentration of D2O (dots) and the best fit of the simplified model (solid line) for a root

742

partly immersed in D2O. The simulated concentrations refer to the root in figure 5. Root

743

length and location of D2O injection are illustrated in figure 7A. A) Average D2O

744

concentration in the root segment immersed in D2O with the best fit of model. B) Average

745

D2O concentration in the root segment beyond the capillary barrier with the best fit of

746

model. C) Average D2O concentration across the root as a function of distance to the root

747

tip at different time steps after D2O injection. Each line refers to a different time step after

748

D2O injection.

749

Figure 7. Schematic representation of the roots measured at daytime and whose results

750

are shown in figure 8.

751

Figure 8. Radial flux into the root as a function of distance from the root tip. The radial

752

flux is calculated for two different sets of root presented in figure 7. Set a refers to the

753

roots that were partly immersed in D2O at the middle parts and the set b refers to the roots

754

that were partly immersed in D2O at the proximal parts. The bar lines show the range of

755

radial fluxes for different positions of root calculated in Zarebadkouki et al. (2013).

756

Figure 9. Neutron radiograph of the sample used during daytime measurement. The

757

radiograph is obtained from stitching four radiographs with marginal overlap. The higher

758

gray value in this radiograph corresponds to the higher soil water content (dark=wet). The

759

compartments marked with stars shows the compartment used for D2O injection during

760

daytime. The bright horizontal and vertical strips show the location of capillary barrier

761

used to stop the transport of D2O in soil. Note that we irrigated the dry compartments

762

one day before the D2O injection experiment started.

763


764 compartment immersed in D2O

compartment beyond the capillary barrier

765 A)

B)

766 767 768 769 770 771 772 773

capillary barrier

774 775 776 777 778 Day: t=60 min

779 Day: t=4 min 780

D)

C)

781 782 783 784 785 30 Night:7, t=60 Night: t=4 minDownloaded from www.plantphysiol.org on September 2014 - min Published by www.plant.org Copyright © 2014 American Society of Plant Biologists. All rights reserved.

786

Figure 1: Neutron radiographs of two samples after injection of 4 ml D2O during day (A and

787

B) and during night (C and D). D2O was injected in one compartment during nighttime and

788

in two compartments during daytime. The images are the differences between the actual

789

radiographs at time t and the radiograph before injection (t=0). Brighter colors indicate lower

790

neutron attenuation and higher D2O/H2O ratio. The images show that: 1) the transport of D2O

791

was faster during day than during night; 2) D2O moved axially beyond the capillary barrier

792

towards the shoot only during day. Images are close-up of the original field of view of

793

15.75×15.75 cm showing the distribution of D2O in the soil and root after D2O injection.

794

Figures are extracted from Zarebanadkouki et al. 2013. (A neutron radiograph of the whole

795

sample used for daytime measurement is given in figure 9).


796 797

A)

798 799 800 801 802

B)

803 804 805 806 807

D)

C)

808 809 810 811 812 813

Figure 2. Illustration of D2O transport into a root partially immersed in D2O. A) Diffusion

814

and convection along a root. Water flows radially till the xylem radius. In the xylem, water

815

flows longitudinally. B) Cross section of a lupine root at a distance of 12 cm from the root

816

tip C)

817

transport model. D) Simplified model in which the different pathways are lumped together

818

in a single averaged pathway across the root tissue. Here, ca and cc are the concentration of

Representation of the root tissue and its effect on D2O transport in the composite


819

D2O in the apoplastic and the symplastic pathway, respectively, cr is the concentration of

820

D2O in the root, Da and Dc are the diffusion coefficient of D2O in the apoplastic pathway and

821

the symplastic pathway, respectively, D is the diffusion coefficient of D2O in the root

822

assuming root as a uniform tissue, jar and jcr are radial flux of water in the apoplastic pathway

823

and the symplastic pathway, respectively, jr is the radial flux of water into the root and Γs

824

the exchange term of D2O between apoplastic and cell to cell pathways.


825 826

A)

827 828 829 830 831 832 833 834 B)

835 836 837 838 839 840 841 842

Figure 3. Sensitivity analysis of the composite transport model. Average concentration of

843

D2O in the root segment immersed in D2O (Fig. 3A) and in the root segment beyond the

844

capillary barrier (Fig. 3B).


845 846 847 848 849 850 851 852 853 854 855 856

Figure 4. Diffusion coefficient of the obtained from the best fit of the simplified model to the

857

experimental data of D2O concentration across the root tissue at nighttime. Note that we

858

assumed that in the first 1.5 cm near the root tip the diffusion of the endodermis is equal to

859

that of the cortex. The data are obtained from 15 roots.

860


861 862

Figure 5. Simulated concentration of D2O across the root tissue at different times after D2O

863

injection. The color bar shows the concentration of D2O in the root. The length of the root

864

and the location of D2O injection is presented in figure 7A.


865 866

A)

B)

R2=0.99

R2=0.95

867 868 869 870 871 872 873

C)

874 875 876 877 878 879 880 881

Figure 6. Measured concentration of D2O (dots) and the best fit of the simplified model (solid

882

line) for a root partly immersed in D2O. The simulated concentrations refer to the root in

883

figure 5. Root length and location of D2O injection are illustrated in figure 7A. A) Average

884

D2O concentration in the root segment immersed in D2O with the best fit of model. B)

885

Average D2O concentration in the root segment beyond the capillary barrier with the best fit

886

of model. C) Average D2O concentration across the root as a function of distance to the root

887

tip at different time steps after D2O injection. Each line refers to a different time step after

888

D2O injection. 37 Downloaded from www.plantphysiol.org on September 7, 2014 - Published by www.plant.org Copyright © 2014 American Society of Plant Biologists. All rights reserved.

889


890 891

Figure 7. Schematic representation of the roots measured at daytime and whose results are

892

shown in figure 8.

893


894 895 896 897 898 899 900 901 902 903 904

Figure 8. Radial flux into the root as a function of distance from the root tip. The radial flux

905

is calculated for two different sets of root presented in figure 7. Set a refers to the roots that

906

were partly immersed in D2O at the middle parts and the set b refers to the roots that were

907

partly immersed in D2O at the proximal parts. The bar lines show the range of radial fluxes

908

for different positions of root calculated in Zarebadkouki et al. (2013).


909 910

Figure 9. Neutron radiograph of the sample used during daytime measurement. The

911

radiograph is obtained from stitching four radiographs with marginal overlap. The higher

912

gray value in this radiograph corresponds to the higher soil water content (dark=wet). The

913

compartments marked with stars shows the compartment used for D2O injection during

914

daytime. The bright horizontal and vertical strips show the location of capillary barrier used


915

to stop the transport of D2O in soil. Note that we irrigated the dry compartments one day

916

before the D2O injection experiment started.


Modeling Root Zone Effects on Preferred Pathways for the Passive Transport of Ions and Water in Plant Roots.

Quantification of osmotic water transport in vivo using fluorescent albumin.

Biophysical rhizosphere processes affecting root water uptake.

Estimation of the hydraulic conductivities of lupine roots by inverse modelling of high-resolution measurements of root water uptake.

Measurement of rates of lipogenesis with deuterated and tritiated water.

Recovering root system traits using image analysis exemplified by two-dimensional neutron radiography images of lupine.

Analysis of Mammalian Cell Proliferation and Macromolecule Synthesis Using Deuterated Water and Gas Chromatography-Mass Spectrometry.

Numerical modeling of water spray suppression of conveyor belt fires in a large-scale tunnel.

In situ quantification and visualization of lithium transport with neutrons.

An Inverse Method to Estimate the Root Water Uptake Source-Sink Term in Soil Water Transport Equation under the Effect of Superabsorbent Polymer.

The composite water and solute transport of barley (Hordeum vulgare) roots: effect of suberized barriers.

Image enhancement using MCNP5 code and MATLAB in neutron radiography.

Apoplastic barrier development and water transport in Zea mays seedling roots under salt and osmotic stresses.

Characterizing roots and water uptake in a ground cover rice production system.

Numerical modeling of ion transport in an ESI-MS system.

Quantification of the types of water in Eudragit RLPO polymer and the kinetics of water loss using FTIR.

Comprehensive Numerical Modeling of Greenhouse Gas Emissions from Water Resource Recovery Facilities.

Radial transport of water across cortical sleeves of excised roots ofZea mays L.

Parameterization of small intestinal water volume using PBPK modeling.

Characterizing the transplanar and in-plane water transport of textiles with gravimetric and image analysis technique: Spontaneous Uptake Water Transport Tester.

Balancing Water Uptake and Loss through the Coordinated Regulation of Stomatal and Root Development.

A mathematical analysis of water and solute transport across the root of Ricinus communis.

Water and sediment transport modeling of a large temporary river basin in Greece.

Mathematical modeling of heat and water transport in human respiratory tract.